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Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 00, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.

Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 00, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 0<x<L, t>0, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.
Transcribed Image Text:Consider the heat equation ди Ət = J²u მ2 subject to the boundary conditions +u, 0<x<L, t>0, u(0,t) = u(L,t) = 0. Suppose 2πx 5πx u(x, 0) = 3 sin - - 8 sin L L where is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x,t). 0047 Does the value of the constant play a role in this limit? Explain.
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